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description=Zvika Brakerski, Professor of Computer Science, Weizmann Institute of Science;
keywords=Zvika Brakerski, Zvika, Brakerski, Zvika Brakerski Home Page, Cryptography, zvika, brakerski, zvika brakerski, zvikab, Weizmann, weizmann, Weizmann Institute of Science, Department of Computer Science and Applied Mathematics, Computer Science, Quantum Computing, bz-sci, bz-sci.com, Stanford, stanford;

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without, efficient, notion, then, other, tcc, possible, use, may, between, protocols, works, its, prove, specifically, results, worst, each, against, used, length, functional, arbitrary, private, approach, prior, however, thus, pseudorandom, when, state, cryptography, into, achieve, simple, study, post, applications, linear, over, particular, circular, depth, multi, very, cannot, vaikuntanathan, free, indistinguishability, adaptive, order, keys, 2018, 2020, consider, either, technique, have, ciphertext, constructing, program, high, vinod, obfuscator, recent, both, adversary, these, solution, bounded, algorithm, entropic, distribution, states, functionality, decryption, kalai, existence, reduction, additional, required, inputs, short, modulus, set, there, well, property, many, randomness, bound, while, messages, hard, parameters, resilient, still, auxiliary, deterministic, efficiently, lpn, lattices, rlwe, io, privacy, np, obtain, properties, stoc, attribute, exist, do, delegation, sub, 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decryption error is allowed an immediate corollary is that known schemes that are based on the hardness of decoding in the presence of noise with low hamming weight cannot be fully homomorphic this applies to known schemes such as lpn based symmetric or public key encryption an additional corollary is that the recent candidate fully homomorphic encryption suggested by bogdanov and lee eprint 11 henceforth bl is insecure in fact we show two attacks on the bl scheme one by applying the aforementioned general statement and another by directly attacking one of the components of the scheme zvika brakerski and yael tauman kalai efficient interactive coding against adversarial noise focs 2012 abstract pdf in this work we study the fundamental problem of constructing interactive protocols that are robust to noise a problem that was originally considered in the seminal works of schulman focs 92 stoc 93 and has recently regained popularity robust interactive communication is the interactive analogue of error correcting codes given an interactive protocol which is designed to run on an error free channel construct a protocol that evaluates the same function or more generally simulates the execution of the original protocol over a noisy channel as in non interactive error correcting codes the noise can be either stochastic i e drawn from some distribution or adversarial i e arbitrary subject only to a global bound on the number of errors we show how to efficiently simulate any interactive protocol in the presence of constant rate adversarial noise while incurring only a constant blow up in the communication complexity cc our simulator is randomized and succeeds in simulating the original protocol with probability at least 1 2 omega cc previous solutions are either inefficient or are resilient only to stochastic noise zvika brakerski fully homomorphic encryption without modulus switching from classical gapsvp crypto 2012 abstract pdf we present a new tensoring technique for lwe based fully homomorphic encryption while in all previous works the ciphertext noise grows quadratically b to b 2 cdot poly n with every multiplication before refreshing our noise only grows linearly b to b cdot poly n we use this technique to construct a emph scale invariant fully homomorphic encryption scheme whose properties only depend on the ratio between the modulus q and the initial noise level b and not on their absolute values our scheme has a number of advantages over previous candidates it uses the same modulus throughout the evaluation process no need for modulus switching and this modulus can take arbitrary form including a power of 2 which carries obvious advantages for implementation in addition security can be classically reduced to the worst case hardness of the gapsvp problem with quasi polynomial approximation factor whereas previous constructions could only exhibit a quantum reduction to gapsvp zvika brakerski craig gentry and vinod vaikuntanathan leveled fully homomorphic encryption without bootstrapping itcs 2012 abstract pdf we present a novel approach to fully homomorphic encryption fhe that dramatically improves performance and bases security on weaker assumptions a central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes capable of evaluating arbitrary polynomial size circuits without gentry s bootstrapping procedure specifically we offer a choice of fhe schemes based on the learning with error lwe or ring lwe rlwe problems that have 2 k security against known attacks for rlwe we have a leveled fhe scheme that can evaluate l level arithmetic circuits with tilde o k cdot l 3 per gate computation i e computation quasi linear in the security parameter security is based on rlwe for an approximation factor exponential in l this construction does not use the bootstrapping procedure a leveled fhe scheme that uses bootstrapping as an optimization where the per gate computation which includes the bootstrapping procedure is tilde o k 2 independent of l security is based on the hardness of rlwe for quasi polynomial factors as opposed to the sub exponential factors needed in previous schemes we obtain similar results to the above for lwe but with worse performance based on the ring lwe assumption we introduce a number of further optimizations to our schemes as an example for circuits of large width e g where a constant fraction of levels have width at least k we can reduce the per gate computation of the bootstrapped version to tilde o k independent of l by batching the bootstrapping operation previous fhe schemes all required tilde omega k 3 5 computation per gate at the core of our construction is a much more effective approach for managing the noise level of lattice based ciphertexts as homomorphic operations are performed using some new techniques recently introduced by brakerski and vaikuntanathan focs 2011 zvika brakerski and vinod vaikuntanathan efficient fully homomorphic encryption from standard lwe focs 2011 abstract pdf we present a fully homomorphic encryption scheme that is based solely on the standard learning with errors lwe assumption applying known results on lwe the security of our scheme is based on the worst case hardness of short vector problems on arbitrary lattices additionally relying on lwe makes our scheme very natural to understand and implement our construction improves on previous works in two aspects we show that somewhat homomorphic encryption can be based on lwe using a new re linearization technique in contrast all previous schemes relied on complexity assumptions related to ideals in various rings we deviate from the squashing paradigm used in all previous works we introduce a new dimension modulus reduction technique which shortens the ciphertexts and reduces the decryption complexity of our scheme em without introducing additional assumptions in contrast all previous works required an additional very strong assumption namely the sparse subset sum assumption our scheme has very short ciphertexts and we therefore use it to construct an asymptotically efficient lwe based single server private information retrieval pir protocol the communication complexity of our protocol in the public key model is k polylog k log db bits per single bit query which is better than any known scheme here k is a security parameter zvika brakerski and yael tauman kalai a parallel repetition theorem for leakage resilience tcc 2012 abstract pdf a leakage resilient encryption scheme is one which stays secure even against an attacker that obtains a bounded amount of side information on the secret key say lambda bits of leakage a fundamental question is whether parallel repetition amplifies leakage resilience namely if we secret share our message and encrypt the shares under two independent keys will the resulting scheme be resilient to 2 lambda bits of leakage surprisingly lewko and waters focs 2010 showed that this is false they gave an example of a public key encryption scheme that is resilient to lambda bits of leakage and yet its 2 repetition is not resilient to even 1 epsilon lambda bits of leakage in their counter example the repeated schemes share secretly generated public parameters in this work we show that under a reasonable strengthening of the definition of leakage resilience one that captures known proof techniques for achieving non trivial leakage resilience parallel repetition does in fact amplify leakage in particular if fresh public parameters are used for each copy of the lewko waters scheme then their negative result does not hold and leakage is amplified by parallel repetition more generally we show that given t schemes that are resilient to lambda_1 ldots lambda_t bits of leakage respectfully their direct product is resilient to sum lambda_i 1 bits we present our amplification theorem in a general framework that applies other cryptographic primitives as well zvika brakerski and vinod vaikuntanathan fully homomorphic encryption from ring lwe and security for key dependent messages crypto 2011 abstract pdf we present a somewhat homomorphic encryption scheme that is both very simple to describe and analyze and whose security quantumly reduces to the worst case hardness of problems on ideal lattices we then transform it into a fully homomorphic encryption scheme using standard squashing and bootstrapping techniques introduced by gentry stoc 2009 one of the obstacles in going from somewhat to full homomorphism is the requirement that the somewhat homomorphic scheme be circular secure namely the scheme can be used to securely encrypt its own secret key for all known somewhat homomorphic encryption schemes this requirement was not known to be achievable under any cryptographic assumption and had to be explicitly assumed we take a step forward towards removing this additional assumption by proving that our scheme is in fact secure when encrypting polynomial functions of the secret key our scheme is based on the ring learning with errors rlwe assumption that was recently introduced by lyubashevsky peikert and regev eurocrypt 2010 the rlwe assumption is reducible to worst case problems on ideal lattices and allows us to completely abstract out the lattice interpretation resulting in an extremely simple scheme for example our secret key is s and our public key is a b as 2e where s a e are all degree n 1 integer polynomials whose coefficients are independently drawn from easy to sample distributions zvika brakerski and gil segev better security for deterministic public key encryption the auxiliary input setting crypto 2011 abstract pdf deterministic public key encryption introduced by bellare boldyreva and o neill crypto 07 provides an alternative to randomized public key encryption in various scenarios where the latter exhibits inherent drawbacks a deterministic encryption algorithm however cannot satisfy any meaningful notion of security when the plaintext is distributed over a small set bellare et al addressed this difficulty by requiring semantic security to hold only when the plaintext has high min entropy from the adversary s point of view in many applications however an adversary may obtain auxiliary information that is related to the plaintext specifically when deterministic encryption is used as a building block of a larger system it is rather likely that plaintexts do not have high min entropy from the adversary s point of view in such cases the framework of bellare et al might fall short from providing robust security guarantees we formalize a framework for studying the security of deterministic public key encryption schemes with respect to auxiliary inputs given the trivial requirement that the plaintext should not be efficiently recoverable from the auxiliary input we focus on hard to invert auxiliary inputs within this framework we propose two schemes the first is based on the decisional diffie hellman and more generally on the d linear assumption and the second is based on a rather general class of subgroup indistinguishability assumptions including in particular quadratic residuosity and paillier s composite residuosity our schemes are secure with respect to any auxiliary input that is subexponentially hard to invert assuming the standard hardness of the underlying computational assumptions in addition our first scheme is secure even in the multi user setting where related plaintexts may be encrypted under multiple public keys constructing a scheme that is secure in the multi user setting even without considering auxiliary inputs was identified by bellare et al as an important open problem zvika brakerski jonathan katz gil segev and arkady yerukhimovich limits on the power of zero knowledge proofs in cryptographic constructions tcc 2011 abstract pdf for over 20 years black box impossibility results have been used to argue the infeasibility of constructing certain cryptographic primitives e g key agreement from others e g one way functions a widely recognized limitation of such impossibility results however is that they say nothing about the usefulness of known non black box techniques this is unsatisfying as we would at least like to rule out constructions using the set of techniques we have at our disposal with this motivation in mind we suggest a new framework for black box constructions that encompasses constructions with a nonblack box flavor specifically those that rely on zero knowledge proofs relative to some oracle we show that our framework is powerful enough to capture the naor yung sahai paradigm for building a shielding cca secure public key encryption scheme from a cpa secure one something ruled out by prior black box separation results on the other hand we show that several black box impossibility results still hold even in a setting that allows for zero knowledge proofs zvika brakerski yael tauman kalai jonathan katz and vinod vaikuntanathan overcoming the hole in the bucket public key cryptography resilient to continual memory leakage focs 2010 abstract pdf in recent years there has been a major effort to design cryptographic schemes that remain secure even if part of the secret key is leaked this is due to a recent proliferation of side channel attacks which through various physical means can recover part of the secret key we explore the possibility of achieving security even with continual leakage i e even if some information is leaked each time the key is used we show how to securely update a secret key while information is leaked we construct schemes that remain secure even if an attacker at each time period can probe the entire memory containing a secret key and leak up to a 1 o 1 fraction of the secret key the attacker may also probe the memory during the updates and leak o log k bits where k is the security parameter relying on subexponential hardness allows k epsilon bits of leakage during each update process all of the above is achieved without restricting the model as is done in previous works e g by assuming that only computation leaks information micali reyzin tcc04 specifically under the decisional linear assumption on bilinear groups which allows for a leakage rate of 1 2 o 1 or the symmetric external diffie hellman assumption which allows for a leakage rate of 1 o 1 we achieve the above for public key encryption identity based encryption and signature schemes prior to this work it was not known how to construct public key encryption schemes even in the more restricted model of mr the main contributions of this work are 1 showing how to securely update a secret key while information is leaked in the more general model and 2 giving a public key encryption and ibe schemes that are resilient to continual leakage zvika brakerski and shafi goldwasser circular and leakage resilient public key encryption under subgroup indistinguishability or quadratic residuosity strikes back crypto 2010 abstract pdf the main results of th...